Think a little
Let be a function which satisfies the above functional equation for all real values of .
If has exactly 3 roots, Find their sum?
The answer is 6054.
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1 solution
If 2 0 1 8 + x is a root, so is 2 0 1 8 − x . So the roots either come in pairs of two that add up to 4 0 3 6 , with one possible exception: x = 2 0 1 8 is a root that pairs with itself.
Since there are three roots, they must consist of one pair and 2 0 1 8 . The sum is 4 0 3 6 + 2 0 1 8 = 6 0 5 4 .